İmdat İşcan

• Prof. Dr.
• Professor (Full) at Giresun University

In this paper, we give a different version of the concept of p-convex functions and obtain some new properties of p-convex functions. Moreover we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are p-convex.

In this paper, the author establishes some new Hermite-Hadamard type inequalities for p-convex functions. Some natural applications to special means of real numbers are also given.

In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that the results of this paper can be reduced to different convexity classes by considering the special cases of M a...

This study is predicated on the exploration of lemmas pertaining to the Hermite-Hadamard-Fejér type integral inequality, focusing on both trapezoidal and midpoint inequalities. It delves into the realm of trigonometrically convex functions and is structured around the foundational lemmas that govern these inequalities. Through rigorous analysis, th...

In this paper, we introduce the notion of generalized n-polynomial P-function. We explore some algebraic properties of this function class. Additionally, we establish a new trapezium type inequality for this generalized class of functions and derive several refinements of the trapezium type inequality for functions whose first derivative in absolut...

In this paper, the concept of Hg-convex function is given for the first time in the literature. Some inequalities of Hadamard’s type for Hg-convex functions are given. Some algebraic properties of Hg-convex functions and special cases are discussed. In addition, we establish some new integral inequalities for Hg-convex functions by using an integra...

In this paper, by using an identity we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is exponential type P-function by using Hölder and power-mean integral inequalities. Then, the aouthors compare the results obtained with both Hölder, Hölder-İşcan integral inequalities and prove that the...

In this study, new lemmas on $p-$convex and $s-p-$convex functions were derived utilizing the integral $\int_{j}^{k} \frac{\left(x^p - j^p\right)^f \left(k^p - x^p\right)^g m(x)}{x^{(f+g)p}} \,dx$. Through this equality, new integral inequalities were established, and novel upper bounds were obtained with the aid of Euler's beta and hypergeometric...

This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Her...

In this paper, we first construct a new generalization of n-polynomial convex function. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of n polynomial convexity. Also, we see that the obtained results in the paper while co...

In this study, by using an integral identity together with both the Hölder and the power-mean inequalities for integrals we establish several new inequalities for differentiable arithmetic-harmonically-convex function. Also, we give some applications for special means.

In this study, we introduce a generalization of P -function, called ( M , P ) -functions, via weighted mean functions given by İşcan. Then, we prove some new inequalities for ( M , P ) -functions. Also, we give new properties for ( M , P ) -functions and present some results for the special cases of M .

In this paper, we introduce a new class of convex functions called n-fractional polynomial p-convex functions. We discuss some properties and present Hermite-Hadamard type inequalities for this generalization. Also when p =-1, our results establish a new definition and Hermite-Hadamard inequalities for n-fractional polynomial harmonically convex fu...

In this paper, we introduce a new class of convex functions so-called n-fractional polynomial s-type functions. We discuss some properties and present Hermite-Hadamard and Ostrowski type inequalities for this generalization with using K-fractional integral operators. Using special cases in our results we get this inequalities for Riemann-Liouville...

In this paper, we introduce a new class of convex functions so-called n-fractional polynomial p-convex functions. We discuss some properties and present Hermite-Hadamard type inequalities for this generalization. Also when p = −1 our results establish new definition and Hermite-Hadamard inequalities for n-fractional polynomial harmonically convex f...

In this paper, we have obtained new Hermite Hadamard Fejer type inequality different from the classical fej ´ er inequality. ´ Thanks to this new inequality, new types of fractional integral inequalities obtained in recent years can be obtained in special cases.

Unfortunately, eleven of our provinces were severely affected due to two severe earthquakes that occurred in our country, the Republic of Turkey, on February 6, 2023. As a result, thousands of buildings were destroyed and tens of thousands of our citizens lost their lives. From past to present, such disasters have occurred in many parts of our worl...

In this manuscript, the authors introduce the concept of the semi P-geometric-arithmetically functions (semi P-GA functions) and give their some algebraic properties. Then, they get Hermite-Hadamard?s integral inequalities for semi P-GA-functions (geometric-arithmetically convex). In addition, the authors obtain new inequalities by using H?lder and...

It is well known that Hermite-Hadamard inequality generates an estimate of the mean value of the convex function over a bounded interval , in this work we investigate some Hermite-Hadamard type integral inequalities for p-convex functions and harmonically convex functions in fractional integral forms. Precisely, we provide extensions better than th...

"In this paper, we introduce and study the concept of strongly n-polynomial convexity functions and their some algebraic properties. We prove two Hermite-Hadamard type inequalities for the newly intro- duced class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolut...

In this work, Hölder-Isçan inequality is used for the class of $ n $-times differentiable $ (s, m) $-convex functions. The outcomes are new Hermite-Hadamard type inequalities and modified integrals are estimated by better bounds. Special cases are deduced as the existing results from literature. Furthermore, some applications to arithmetic, geometr...

In this paper, some new integral inequalities for integrable geometrically convex mappings via the general forms of proportional fractional integral operators are proved. Basic definitions, various classical inequalities and generalized proportional fractional integral operators are used to prove the main findings.

In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value,...

The aim of this article is to define a special case of h- convex function, namely the notion of a trigonometrically convex function. Using the Hölder, Hölder-İşcan integral inequality and the power-mean, improved power-mean integral inequalities, and together with an integral identity, some new Simpson-type inequalities have been obtained for trigo...

In this paper, firstly, we give some historical backgorunds and futher information about AG−convexity, Riemann Liouville fractional integral operators and general forms of proportional fractional integral operators. In the second part, we have used the general forms of proportional fractional integral operators to prove new integral inequalities fo...

In this study, some inequalities of Hermite Hadamard type obtained for p-convex functions are given for Lipschitz mappings. Also, some applications for special means have been given.

Abstract In this paper, firstly, we prove a Jensen–Mercer inequality for GA-convex functions. After that, we establish weighted Hermite–Hadamard’s inequalities for GA-convex functions using the new Jensen–Mercer inequality, and we establish some new inequalities connected with Hermite–Hadamard–Mercer type inequalities for differentiable mappings wh...

In this paper, first, we prove the weighted Hermite–Hadamard–Mercer inequalities for convex functions, after we establish some new weighted inequalities connected with the right‐sides of weighted Hermite–Hadamard–Mercer type inequalities for differentiable functions whose derivatives in absolute value at certain powers are convex. The results prese...

In this work, by using an integral identity together with the Hölder–İşcan inequality we establish several new inequalities for n-times differentiable convex and concave mappings. Furthermore, various applications for some special means as arithmetic, geometric, and logarithmic are given.

Abstract The celebrated Hermite–Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite–Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some...

In this study, the assumption of being differentiable for the convex function f in the (p, q)-Hermite-Hadamard inequality is removed. A new identity for the right-hand part of (p, q)-Hermite-Hadamard inequality is proved. By using established identity, some (p, q)-trapezoid integral inequalities for convex and quasi-convex functions are obtained. T...

In this paper, the authors give a new concept which is a generalization of the concepts s-convexity, GA − s-convexity, harmonically s-convexity and (p, s)-convexity establish some new Hermite-Hadamard type inequalities for this class of functions. Some natural applications to special means of real numbers are also given.

In this paper, …rstly, we prove the Jensen-Mercer inequality for GA-convex functions, after we establish weighted Hermite-Hadamard's inequalities for GA-convex functions using new Jensen-Mercer inequality and we establish some new inequalities connected with the right-sides of Hermite-Hadamard type inequalities for di¤erentiable mappings whose deri...

In this paper, …rstly, we prove the weighted Hermite-Hadamard-Mercer inequalities for convex functions, after we establish some new weighted inequalities connected with the right-sides of weighted Hermite-Hadamard-Mercer type inequalities for di¤erentiable functions whose derivatives in absolute value at certain powers are convex. The results prese...

Abstract In this manuscript, we give and study the concept of exponential type convex functions and some of their algebraic properties. We prove two Hermite–Hadamard (H-H) type integral inequalities for the newly introduced class of functions. We also obtain some refinements of the H-H inequality for functions whose first derivative in absolute val...

In this paper, a new improvement of celebrated Hölder inequality using isotonic linear functionals is established. An important feature of the new inequality obtained here is that many existing inequalities related to the Hölder inequality can be improved which we also illustrate with an application.

In this paper, we introduce and study the concept of n-polynomial convexity functions and their some algebric properties. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, rais...

Abstract In this paper, we establish new refinements for integral and sum forms of Hölder inequality. Many existing inequalities related to the Hölder inequality can be improved via newly obtained inequalities, which we illustrate by an application.

In this paper, by using an integral identity some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose second derivatives in absolute value at certain power are arithmetically-harmonically convex are obtained. Some applications to special means of real numbers are also given.

In this paper, with a new approach, new fractional Hermite-Hadamard type inequality for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlie...

Abstract In this paper, we establish some new integral inequalities of Hermite–Hadamard type for s-convex functions by using the Hölder–İşcan integral inequality. We also compare our new results with the known results and show that the results which we obtained are better than the known results. Finally, we give some applications to trapezoidal for...

In this paper, we give the correct quantum Hermite-Hadamard type inequality for the functions of two variables over finite rectangles. We provide some quantum estimates between the middle and the leftmost terms in correct quantum Hermite-Hadamard inequalities of functions of two variables using convexity and quasi-convexity on the coordinates .

In this paper, firstly the authors establish Hermite-Hadamard inequality for p-convex functions via Katugampola fractional integrals. Then a new identity involving Katugampola fractional integrals is proved. By using this identity, some new Hermite-Hadamard type inequalities for classes of p-convex functions are obtained.

In this study are investigated p-convex stochastic processes which are extensions of convex stochastic processes. A suitable example is also given for this process. In addition, in this case a p-convex stochastic process is increasing or decreasing, the relation with convexity is revealed. The concept of inequality as convexity has an important pla...

In this paper, new improvement of celebrated Hölder inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the Hölder inequality can be improved via new improvement of Hölder inequality. We also show this in an application.

In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejér inequality are just results of Hermite-Hadamard-Fejér inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard-Fejér inequality and better than given in [9] by Sarıkaya et al. is obtaine...

In this paper, we introduce a new the concept called as the sym-metrized GA-convex function, give Hermite-Hadamard's inequalities for sym-metrized GA-convex functions. Furthermore, we establish Hermite-Hadamard type inequalites for the product of a GA-convex function with a symmetrized GA-convex function and also for two symmetrized GA-convex funct...

In this paper, the author introduces the concept of the symmetrized p-convex function, gives Hermite-Hadamard type inequalities for symmetrized p-convex functions.

In this study, we introduce a new class of functions called as mul-tiplicatively harmonically P-function. Some new Hermite-Hadamard type inequalities are obtained for this class of functions.

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-· I¸scanI¸scan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex...

In this paper, new re…nements for integral and sum forms of Hölder inequality are established. We note that many existing inequalities related to the Hölder inequality can be improved via obtained new inequalities in here, we show this in an application

In this paper, we introduce a new the concept called the symmetrized GA-convex function and give Hermite-Hadamard?s inequalities for symmetrized GA-convex functions. Furthermore, we establish Hermite-Hadamard type inequalites for the product of a GA-convex function with a symmetrized GAconvex function and also for two symmetrized GA-convex function...

In this paper, we introduce a new class of extended multiplicatively geometrically P-function. Some new Hermite-Hadamard type inequalities are derived. Results represent significant refinement and improvement of the previous results.

In this paper we obtain the Hermite-Hadamard Inequality for MϕA-strongly convex function. Using this MϕA−strongly convex function we get some new theorems and corollaries.

In this paper, we have obtained new Hermite Hadamard Fejér type inequality different from the classical fejér inequality. With the help of this inequality, we have achieved Hermite Hadamard inequality for all of the Riemann Liouville and Conformable fractional integral that are both available and connot be obtained.

In this paper, we establish an identity for n-times differentiable functions via Riemann-Liouville fractional integrals. By using this new identity, we have some new results about trapezoid type inequalities for n-times differentiable convex functions via Riemann-Liouville fractional integrals. The results, given here extended the results given the...

In this paper we obtain the Hermite-Hadamard Inequality for strongly GA-convex function. Using this strongly GA-convex function we get the new theorem and corollary. 2010 AMS Classification: 26A51, 26D07, 39B62.

In this paper, we prove the correct (p, q)-Hermite–Hadamard inequality, some new (p, q)-Hermite–Hadamard inequalities, and generalized (p, q)-Hermite–Hadamard inequality. By using the left hand part of the correct (p, q)-Hermite–Hadamard inequality, we have a new equality. Finally using the new equality, we give some (p, q)-midpoint type integral i...

This paper is about obtaining some new type of integral inequalities for functions from the Lipschitz class. For this, some new integral inequalities related to the differences between the two different types of integral averages for Lipschitzian functions are obtained. Moreover, applications for some special means as arithmetic, geometric, logarit...

In this paper, it is given a new concept which is a generalization of the concepts s-convexity, M ϕ A-convexity, M ϕ As -convexity and obtained some theorems for Hermite-Hadamard type inequalities for this class of functions. Some natural applications to special means of real numbers are also given.

In this paper we obtain the Hermite-Hadamard Inequality for strongly p-convex function. Using this strongly p-convex function we get the new theorem and corollary.

In this paper we obtain the Hermite-Hadamard Inequality for strongly GA-convex function. Using this strongly GA-convex function we get the new theorem and corollary.

In this paper we obtain the Hermite-Hadamard Inequality for strongly p-convex function. Using this strongly p-convex function we get the new theorem and corollary.

In this paper, a fractional Hermite-Hadamard type inequality and two different fractional Hermite-Hadamard-Fejer type inequalities for GA-convex functions are proved. Also, two identity for differentiable functions are obtained. By using this two identity, some trapezoid and midpoint type errors estimations for GA-convex functions in fractional int...

In this paper, we prove the correct q-Hermite-Hadamard inequality, some new q-Hermite-Hadamard inequalities, and generalized q-Hermite-Hadamard inequality. By using the left hand part of the correct q-Hermite-Hadamard inequality, we have a new equality. Finally using the new equality, we give some q-midpoint type integral inequalities through q-dif...

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequality for convex functions is obtained by using only the right Riemann-Liouville fractional integral. Also, to have new fractional trape-zoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize th...

In this study, we obtained the Hermite-Hadamard integral inequality for MφA-P-function. Then we gave a new identity for MφA-P-function and using these identity, we obtained the theorems and the results.

Differentiation and integration are basic operations of calculus and analysis. Indeed, they are in- finitesimal versions of substraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, converting the roles of substraction and addition i...

In this paper, firstly, Hermite–Hadamard–Fejér type inequalities for p-convex functions in fractional integral forms are built. Secondly, an integral identity and some Hermite–Hadamard–Fejér type integral inequalities for p-convex functions in fractional integral forms are obtained. Finally, some Hermite–Hadamard and Hermite–Hadamard–Fejér inequali...

Bu çalışmada, Hölder integral eşitsizliği ile birlikte bir integral eşitliği kullanılarak n-kere türevlenebilen Godunova-Levin Fonksiyonları için bir kaç yeni eşitsizlik bulunmuştur.