Integral Inequalities and Generalized Convexity

Shashi Kant Mishra Ph.D., D.Sc. is Professor at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, with over 24 years of teaching experience. He has authored eight books, including textbooks and monographs, and has been on the editorial boards of several important international journals. He has guest edited special issues of the Journal of Global Optimization; Optimization Letters (both Springer Nature) and Optimization (Taylor & Francis). He has received INSA Teacher Award 2020 from Indian National Science Academy, New Delhi and DST Fast Track Fellow 2001 from Ministry of Science and Technology, Government of India. Prof. Mishra has published over 203 research articles in reputed international journals and supervised 21 Ph.D. students. He has visited around 15 institutes/ universities in countries such as France, Canada, Italy, Spain, Japan, Taiwan, China, Singapore, Vietnam, and Kuwait. His current research interest includes mathematical programming with equilibrium, vanishing and switching constraints, invexity, multiobjective optimization, nonlinear programming, linear programming, variational inequalities, generalized convexity, integral inequalities, global optimization, nonsmooth analysis, convex optimization, nonlinear optimization, and numerical optimization. Nidhi Sharma is Fellow of the Council of Scientific Industrial Research (CSIR) at the Department of Mathematics, Institute of Science, Varanasi, India. She received the M.Sc. degree in Mathematics from Banaras Hindu University, Varanasi, India. She is working on generalized convexity and integral inequalities under the supervision of Prof. S. K. Mishra. Her current research interests include integral inequalities, generalized convexities, set valued functions, and stochastic process. Jaya Bisht is DST INSPIRE Fellow (Senior Research Fellow) at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India. She received BSc. and M.Sc. degree in Mathematics from Hemwati Nandan Bahuguna Garhwal University (Central University), Srinagar, India. She is awarded Junior Research Fellowship (JRF) from Human Resource Development Group of Council of Scientific Industrial Research (HRD-CSIR), Government of India. Her current research interest includes integral inequalities, generalized convexities, Set valued functions, and stochastic process.

1. Introduction. 2. Integral Inequalities for Strongly Generalized Convex Functions. 3. Integral Inequalities for Strongly Generalized Convex Functions of Higher Order. 4. Integral Inequalities for Generalized Preinvex Functions. 5. Some Majorization Integral Inequalities for Functions Defined on Rectangles via Strong Convexity. 6. Hermite-Hadamard type Inclusions for Interval-Valued Generalized Preinvex Functions. 7. Some Inequalities for Multidimensional General h-Harmonic Preinvex and Strongly Generalized Convex Stochastic Processes. 8. Applications.