Some well known inequalities for $ (h_1, h_2) $-convex stochastic process via interval set inclusion relation-Reference-Cited by-同舟云学术

Some well known inequalities for $ (h_1, h_2) $-convex stochastic process via interval set inclusion relation

Published:2023 Issue:9 Volume:8 Page:19913-19932
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Afzal Waqar¹,Abbas Mujahid¹²³,Eldin Sayed M.⁴,Khan Zareen A.⁵

Affiliation:

1. Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan

2. Department of Medical Research, China Medical University, Taichung, Taiwan

3. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa

4. Center of Research, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt

5. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Abstract

<abstract><p>This note introduces the concept of $ (h_1, h_2) $-convex stochastic processes using interval-valued functions. First we develop Hermite-Hadmard $ (\mathbb{H.H}) $ type inequalities, then we check the results for the product of two convex stochastic process mappings, and finally we develop Ostrowski and Jensen type inequalities for $ (h_1, h_2) $-convex stochastic process. Also, we have shown that this is a more generalized and larger class of convex stochastic processes with some remark. Furthermore, we validate our main findings by providing some non-trivial examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference56 articles.

1. R. E. Moore, Interval analysis, Englewood Cliffs, Prentice-Hall, 1966.

2. N. A. Gasilov, Ş. E. Amrahov, Solving a nonhomogeneous linear system of interval differential equations, Soft Comput., 22 (2018), 3817–3828.

3. D. Singh, B. A. Dar, Sufficiency and duality in non-smooth interval valued programming problems, J. Ind. Manag. Optim., 15 (2019), 647–665. https://doi.org/10.3934/jimo.2018063

4. E. de Weerdt, Q. P. Chu, J. A. Mulder, Neural network output optimization using interval analysis, IEEE T. Neural Networ., 20 (2009), 638–653. http://doi.org/10.1109/TNN.2008.2011267

5. K. Nikodem, On convex stochastic processes, Aequationes Math., 2 (1998), 427–446. https://dx.doi.org/10.1007/BF02190513

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