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2. A Unified Approach to Extended General Quasi Variational Inclusions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Advisory Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, Rassias, Michael Th., editor, and Zographopoulos, Nikolaos B., editor

Published
2023
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5. On G (σ, h) -Convexity of the Functions and Applications to Hermite-Hadamard’s Inequality

Author

Awan, Muhammad Uzair, Noor, Muhammad Aslam, Noor, Khalida Inayat, Chu, Yu-Ming, Ellahi, Sara, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2022
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6. General Preinvex Functions and Variational-Like Inequalities

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Mohsen, Bandar, Rassias, Michael Th., Raigorodskii, Andrei, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2022
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9. Some integral inequalities for generalized left and right log convex interval-valued functions based upon the pseudo-order relation

Author

Khan Muhammad Bilal, Noor Muhammad Aslam, Macías-Díaz Jorge E., Soliman Mohamed S., and Zaini Hatim Ghazi

Subjects
left and right log-s-convex interval-valued functions, hermite-hadamard-type inequality, hermite-hadamard-fejér-type inequality, jensen’s inequality, 26a33, 26a51, 26d10, Mathematics, QA1-939
Abstract

It is a well-known fact that inclusion and pseudo-order relations are two different concepts which are defined on the interval spaces, and we can define different types of convexities with the help of both relations. By means of pseudo-order relation, the present article deals with the new notions of convex functions which are known as left and right log-ss-convex interval-valued functions (IVFs) in the second sense. The main motivation of this study is to present new inequalities for left and right log-ss-convex-IVFs. Therefore, we establish some new Jensen-type, Hermite-Hadamard (HH)-type, and Hermite-Hadamard-Fejér (HH-Fejér)-type inequalities for this kind of IVF, which generalize some known results. To strengthen our main results, we provide nontrivial examples of left and right log-ss-convex IVFs.

Published
2022
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14. Some New Classes of Higher Order Strongly Generalized Preinvex Functions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Parasidis, Ioannis N., editor, Providas, Efthimios, editor, and Rassias, Themistocles M., editor

Published
2021
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15. Characterizations of Higher Order Strongly Generalized Convex Functions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Rassias, Michael Th., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, and Rassias, Themistocles M., editor

Published
2021
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16. Higher Order Strongly m-convex Functions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, and Rassias, Themistocles M., editor

Published
2021
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17. Properties of Exponentially m-Convex Functions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, and Rassias, Themistocles M., editor

Published
2021
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18. Relative Strongly Exponentially Convex Functions

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Rassias, Themistocles M., Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Vu, Van, Advisory Editor, Vrahatis, Michael N., Associate Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, and Rassias, Themistocles M., editor

Published
2021
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25. From Representation Theorems to Variational Inequalities

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Pardalos, Panos M., Series Editor, Thai, My T., Series Editor, Du, Ding-Zhu, Honorary Editor, Belavkin, Roman V., Advisory Editor, Birge, John R., Advisory Editor, Butenko, Sergiy, Advisory Editor, Giannessi, Franco, Advisory Editor, Kumar, Vipin, Advisory Editor, Nagurney, Anna, Advisory Editor, Pei, Jun, Advisory Editor, Prokopyev, Oleg, Advisory Editor, Rebennack, Steffen, Advisory Editor, Resende, Mauricio, Advisory Editor, Terlaky, Tamás, Advisory Editor, Van, Vu, Advisory Editor, Xue, Guoliang, Advisory Editor, Ye, Yinyu, Advisory Editor, Daras, Nicholas J., editor, and Rassias, Themistocles M., editor

Published
2020
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26. Series solution to fractional contact problem using Caputo’s derivative

Author

Rafiq Muhammad, Noor Muhammad Aslam, Farwa Shabieh, Kamran Muhammad, Saeed Faisal, Gepreel Khaled A., Yao Shao-Wen, and Ahmad Hijaz

Subjects
fractional contact problem, obstacle, variational iteration method, caputo’s fractional derivative, Physics, QC1-999
Abstract

In this article, contact problem with fractional derivatives is studied. We use fractional derivative in the sense of Caputo. We deploy penalty function method to degenerate the obstacle problem into a system of fractional boundary value problems (FBVPs). The series solution of this system of FBVPs is acquired by using the variational iteration method (VIM). The performance as well as precision of the applied method is gauged by means of significant numerical tests. We further study the convergence and residual errors of the solutions by giving variation to the fractional parameter, and graphically present the solutions and residual errors accordingly. The outcomes thus obtained witness the high effectiveness of VIM for solving FBVPs.

Published
2021
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27. Harmonic Exponential Convex Functions and Inequalities

Author

Awan, Muhammad Uzair, Noor, Muhammad Aslam, Noor, Khalida Inayat, Pardalos, Panos M., Managing Editor, Du, Ding-Zhu, Honorary Editor, Birge, J., Advisory Editor, Butenko, S., Advisory Editor, Giannessi, F., Advisory Editor, Rebennack, S., Advisory Editor, Terlaky, T., Advisory Editor, Ye, Y., Advisory Editor, Andrica, Dorin, editor, and Rassias, Themistocles M., editor

Published
2019
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28. Iterative Methods for Variational Inequalities

Author

Noor, Muhammad Aslam, Noor, Khalida Inayat, Rassias, Themistocles M., Pardalos, Panos M., Managing Editor, Du, Ding-Zhu, Honorary Editor, Birge, J., Advisory Editor, Butenko, S., Advisory Editor, Giannessi, F., Advisory Editor, Rebennack, S., Advisory Editor, Terlaky, T., Advisory Editor, Ye, Y., Advisory Editor, Andrica, Dorin, editor, and Rassias, Themistocles M., editor

Published
2019
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44. NEW ITERATIVE SCHEMES FOR GENERAL HARMONIC VARIATIONAL INEQUALITIES.

Author

NOOR, MUHAMMAD ASLAM and NOOR, KHALIDA INAYAT

Subjects
*CONVEX sets, *HARMONIC functions, *VARIATIONAL inequalities (Mathematics), *CONVEX functions, *SET functions
Abstract

Some new classes of general harmonic convex sets and convex functions are introduced and studied in this paper. The optimality criteria of the differentiable general harmonic functions is characterized by the general harmonic variational inequalities. Special cases are also pointed out as applications of the new concepts. Auxiliary principle technique involving an arbitrary operator is applied to suggest and analysis several inertial type methods are suggested. Convergence criteria is investigated of the proposed methods under weaker conditions. The results obtained in this paper may inspire further research along with implementable numerical methods for solving the general harmonic variational inequalities and related optimization problems. [ABSTRACT FROM AUTHOR]

Published
2024
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45. ANALYTIC INEQUALITIES INVOLVING WEIGHTED EXPONENTIAL -BETA FUNCTIONS AND APPLICATIONS.

Author

CHU, YU-MING, AWAN, MUHAMMAD UZAIR, JAVED, MUHAMMAD ZAKRIA, BRAHIM, KAMEL, NOOR, MUHAMMAD ASLAM, and RAISSOULI, MUSTAPHA

Subjects
MATHEMATICAL inequalities, CONVEX functions, SPECIAL functions, INTEGRAL inequalities, EXPONENTIAL functions, DIFFERENTIAL equations
Abstract

Integral inequalities are the proficient aspect of mathematical analysis. Various techniques have been deployed to acquire to fresh inequalities which are beneficial in various area problems. The aim of this paper is to derive some new analytic inequalities involving generalized weighted exponential beta functions. To attain our primary objectives, we introduce the generalized exponential function X and weighted form of exponential beta functions Furthermore, we briefly discuss their properties. we derive several inequalities in association with As the applications of these new developments,we conclude some error estimates of Ostrwoski's type inequalities, which show the significance of the obtained results. [ABSTRACT FROM AUTHOR]

Published
2024
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