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FURTHER ON PETROVIĆ'S TYPES INEQUALITIES
IQBAL, WASIM,REHMAN, ATIQ UR,FARID, GHULAM,RATHOUR, LAXMI,SHARMA, M.K.,MISHRA, VISHNU NARAYAN The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6
In this article, authors derived Petrović's type inequalities for a class of functions, namely, called exponentially h-convex functions. Also, the associated results for coordinates has been derived by defining exponentially h-convex functions on coordinates.
Saima Rashid,Muhammad Aslam Noor,Khalida Inayat Noor 강원경기수학회 2019 한국수학논문집 Vol.27 No.4
In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fej\'{e}r type inequalities for the exponentially $(\hbar,\mathfrak{m})$-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.
K. Vijaya,G. Murugusundaramoorthy,N. E. Cho 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.1
The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.
Generalization of Jensen's inequality by Euler's identity and related results
G. Aras-Gazić,J. Pecarić,A. Vukelić 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.2
In this paper we consider n-convex funtions. Using Euler`s identity, the result concering for Jensen`s inequality and converses of Jensen`s inequality for signed measure are presented. As a consequence, also the results concerning to the Hermite-Hadamard inequalities are presented. Using these inequlities, we produce new expenentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied.
FUNCTIONS SUBORDINATE TO THE EXPONENTIAL FUNCTION
Priya G. Krishnan,Vaithiyanathan Ravichandran,Ponnaiah Saikrishnan Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.1
We use the theory of differential subordination to explore various inequalities that are satisfied by an analytic function p defined on the unit disc so that the function p is subordinate to the function e<sup>z</sup>. These results are applied to find sufficient conditions for the normalised analytic functions f defined on the unit disc to satisfy the subordination zf'(z)/f(z) ≺ e<sup>z</sup>.
HIGHER ORDER STRONGLY EXPONENTIALLY PREINVEX FUNCTIONS
NOOR, MUHAMMAD ASLAM,NOOR, KHALIDA INAYAT The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.3
In this paper, some new classes of the higher order strongly exponentially preinvex functions are introduced. New relationships among various concepts of higher order strongly exponentially preinvex functions are established. It is shown that the optimality conditions of differentiable higher order strongly exponentially preinvex functions can be characterized by exponentially variational-like inequalities. Parallelogram laws for Banach spaces are obtained as an application. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previously known results.
The Extension Problem for Exponentially Convex Functions
A. M. Zabel,Maha A. Bajnaid 경북대학교 자연과학대학 수학과 2004 Kyungpook mathematical journal Vol.44 No.1
Our main result is to prove that every exponentially convex function dened on an open nonempty connected subset of a connected Lie group G can be extended to an exponentially convex function on all G.
Extensing of Exponentially Convex Function on the Heisenberg Group
Zabel, A.M.,Bajnaid, Maha A. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.4
The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].
Generalizations of Sherman's theorem by Montgomery identity and new Green functions
M. ADIL KHAN,JAMROZ KHAN,J. Pecaric 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.4
In this paper, we give generalization of Sherman inequality by using Green functions and Montgomery identity. We present Gruss and Ostrowski-type inequalities related to generalized Sherman inequality. We give mean value theorems and n-exponential convexity for the functional associated to generalized inequality. We also give a family of functions which support our results for exponentially convex functions and construct a class of means.
ALI, HODA A. 대한수학회 2006 Kyungpook mathematical journal Vol.46 No.3
In the present paper we shall prove that on a foundation *-semigroup S with an identity and with a locally bounded Borel measurable weight function ω, the pointwise convergence and the uniform convergence of a sequence of ω-bounded exponentially convex functions on S which are also continuous at the identity are equivalent.