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13 results on '"Muharrem Tomar"'

1. Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals

Author

Praveen Agarwal, Mohamed Jleli, and Muharrem Tomar

Subjects
Hermite-Hadamard inequality, generalized k-fractional integral, ( k , s ) $(k, s)$ -fractional integral, ( k , s ) $(k, s)$ -Riemann-Liouville fractional integral, Mathematics, QA1-939
Abstract

Abstract Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named ( k , s ) $(k,s)$ -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

Published
2017
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2. Certain inequalities associated with Hadamard k-fractional integral operators

Author

Muharrem Tomar, Shahid Mubeen, and Junesang Choi

Subjects
Mathematics, QA1-939
Abstract

Abstract We aim to present some new Pólya-Szegö type inequalities associated with Hadamard k-fractional integral operators, which are also used to derive some Chebyshev type integral inequalities. Further we apply some of the results presented here to a function which is bounded by the Heaviside functions.

Published
2016
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3. Hermite-Hadamard type inequalities for generalized convex functions on fractal sets style

Author

Muharrem Tomar, Praveen Agarwal, and Junesang Choi

Subjects
Fractal sets, Generalized convex functions, Generalized Hermite--Hadamard inequality, Generalized Holder inequality, Mathematics, QA1-939
Abstract

We aim to establish certain generalized Hermite-Hadamard's inequalities for generalized convex functions via local fractional integral. As special cases of some of the results presented here, certain interesting inequalities involving generalized arithmetic and logarithmic means are obtained.

Published
2018
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5. Certain Ostrowski type inequalities for generalized s-convex functions

Author

Bessem Samet, Praveen Agarwal, Muharrem Tomar, and Mohamed Jleli

Subjects
Pure mathematics, Algebra and Number Theory, Inequality, media_common.quotation_subject, 010102 general mathematics, Type (model theory), 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, 0101 mathematics, Convex function, Analysis, Mathematics, media_common
Published
2017
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6. $${\varvec{(k,s)}}$$ ( k , s ) -Riemann–Liouville fractional integral inequalities for continuous random variables

Author

Selahattin Maden, Muharrem Tomar, and Erhan Set

Subjects
Pure mathematics, Inequality, General Mathematics, media_common.quotation_subject, 020206 networking & telecommunications, Field (mathematics), 0102 computer and information sciences, 02 engineering and technology, Variance (accounting), Riemann liouville, 01 natural sciences, Combinatorics, Probability theory, 010201 computation theory & mathematics, 0202 electrical engineering, electronic engineering, information engineering, Random variable, Mathematics, media_common
Abstract

In this paper, we introduce some new concepts to the field of probability theory: \(\left( k,s\right) \)-Riemann–Liouville fractional expectation and variance functions. Some generalized integral inequalities are established for \(\left( k,s\right) \)-Riemann–Liouville expectation and variance functions.

Published
2016
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7. Hermite-Hadamard Type Inequalities for s-Convex Stochastic Processes in the Second Sense

Author

Erhan Set, Muharrem Tomar, and Selahattin Maden

Subjects
Convex analysis, Combinatorics, Doubly stochastic matrix, Continuous-time stochastic process, Stochastic calculus, Applied mathematics, Discrete-time stochastic process, Stochastic optimization, Subderivative, Stochastic approximation, Mathematics
Abstract

In this study, s-convex stochastic processes in the second sense are presented and some well-known results concerning s-convex functions are extended to s-convex stochastic processes in the second sense. Also, we investigate relation between s-convex stochastic processes in the second sense and convex stochastic processes.

Published
2014
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8. Some Reverse Hölder Type Inequalities Involving $$(k,s)-$$ ( k , s ) - Riemann-Liouville Fractional Integrals

Author

Praveen Agarwal, Shilpi Jain, Gradimir V. Milovanović, and Muharrem Tomar

Subjects
Hölder's inequality, Pure mathematics, Inequality, media_common.quotation_subject, Type (model theory), Riemann liouville, Reverse holder inequality, media_common, Mathematics
Abstract

In this paper, we aim to present the improved version of the reverse Holder type inequalities by taking \((k,s)-\)Riemann-Liouville fractional integrals. Furthermore, we also discuss some applications of Theorem 1 using some types of fractional integrals.

Published
2017
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9. Certain Hermite-Hadamard type inequalities via generalized

Author

Praveen, Agarwal, Mohamed, Jleli, and Muharrem, Tomar

Subjects
Hermite-Hadamard inequality, 26D15, Research, 26A51, generalized k-fractional integral, 26A33, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k, s)$\end{document}(k,s)-Riemann-Liouville fractional integral, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k, s)$\end{document}(k,s)-fractional integral
Abstract

Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(k,s)$\end{document}(k,s)-Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established. Also, by using the obtained identity, we get a Hermite-Hadamard type inequality.

Published
2016

10. New inequalities of Hermite-Hadamard type for generalized quasi-convex functions with applications

Author

Muharrem Tomar, Erhan Set, and Nazlı Uygun

Subjects
Discrete mathematics, Class (set theory), Pure mathematics, Hermite polynomials, Inequality, Hadamard transform, media_common.quotation_subject, Mathematics::Classical Analysis and ODEs, Type (model theory), Convex function, Convexity, media_common, Mathematics
Abstract

In this paper, we consider the class of generalized quasi-convex. Then using this convexity, we obtain some new generalized Hermite-Hadamard type integral inequalities for the generalized quasi-convex functions.

Published
2016
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11. Hermite-Hadamard Type Riemann-Liouville Fractional Integral Inequalities for Convex Functions

Author

Muharrem Tomar, M. Zeki Sarikaya, and Erhan Set

Subjects
Lemma (mathematics), Pure mathematics, Hermite polynomials, Hadamard transform, Mathematical analysis, Mathematics::Classical Analysis and ODEs, Aubin–Lions lemma, Céa's lemma, Riemann liouville, Convex function, Mathematics, Fractional calculus
Abstract

International Conference on Advances in Natural and Applied Sciences (ICANAS) -- APR 21-23, 2016 -- Antalya, TURKEY SET, ERHAN/0000-0003-1364-5396 WOS: 000376001000035 In this paper, we prove a useful lemma. After that, using this lemma, we obtain several new Hermite-Hadamard type of inequalities for Reimann-Liouville fractional integrals.

Published
2016

12. On generalized Gruss type inequalities for k-fractional integrals

Author

Mehmet Zeki Sarikaya, Erhan Set, and Muharrem Tomar

Subjects
Computational Mathematics, Pure mathematics, Applied Mathematics, Calculus, Integral inequalities, Type (model theory), Weighted Gruss inequality, k- Reimann-Liouville fractional integral, Mathematics
Abstract

SET, ERHAN/0000-0003-1364-5396 WOS: 000361771500005 The aim of the present paper is to investigate some new integral inequalities of Gruss type for k - Riemann-Liouville fractional integrals. From our results, new weighted or classical Griiss type inequalities have been established for some special cases. Moreover, special cases of the integral inequalities in this paper have been obtained by Dahmani and Tabharit, 2010 in [5]. (C) 2015 Elsevier Inc. All rights reserved.

Published
2015

13. Some new integral inequalities for \(k\)-fractional integrals

Author

Jessada Tariboon, Sotiris K. Ntouyas, Muharrem Tomar, Jessada Tariboon, Sotiris K. Ntouyas, and Muharrem Tomar

Abstract

The aim of the present paper is to investigate some new integral inequalities for \(k\)-fractional integrals. Moreover, special cases of the integral inequalities in this paper have been obtained by Tariboon et.al. in [22].

Published
2016

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