No abstract

"In this paper, we study the existence of solutions of equilibrium problems in the setting of Hadamard manifolds under the pseudomonotonicity and geodesic upper sign continuity of the equilibrium bifunction and under different kinds of coercivity conditions. We also study the existence of solutions of the equilibrium problems under properly quasimonotonicity of the equilibrium bifunction. We propose a two-step proximal point algorithm for solving equilibrium problems in the setting of Hadamard manifolds. The convergence of the proposed algorithm is studied under the strong pseudomonotonicity and Lipschitz-type condition. The results of this paper either extend or generalize several known results in the literature."

In this paper, we consider and study a system of generalized variational inclusions involving Cayley operators and an XOR-operation in q-uniformly smooth Banach spaces. To obtain the solution of the system of generalized variational inclusions involving Cayley operators and an XOR-operation, we use some properties of Cayley operators as well as an XOR-operation. We also discuss the convergence criterion. In support of our main result, we provide an example.

The COVID-19 pandemic continues to distress the Indian economy across verticals and sectors, including the entertainment industry. These sectors have been witnessing massive disruptions over the past few months across the consumer value chain. Due to the increase in complexities in living standards, individuals are exploring alternatives for entertainment. Less available time for family, more workload during weekends, less vacation is some of the factors people are staying away from vising cinema halls. We have also observed radical changes in consumers’ behavior, perception, preferences during and after the lockdown as they have continued to study and work from home The study focuses on the changing consumer preference to OTT over traditional mediums of media viewing such as cinemas and multiplexes. While a silent trend over the last 3 years, it has been accelerated due to the ongoing pandemic. OTT or Over the Top refers to mediums offering television and media consumption over the internet. While the shift is visible, this project aims to enlist the reasons for this change and the factors that drive it. In this context, the author is making an attempt to explore the root cause of the Paradigm shift of people's preferences to OTT Platforms versus Multiplexes during pandemics. Primary and Secondary data are the main sources of collection of data. The secondary data is collated and compiled from both published and unpublished resources.

This is the first paper dealing with the study of minimum and maximum principle sufficiency properties for nonsmooth variational inequalities by using gap functions in the setting of Hadamard manifolds. We also provide some characterizations of these two sufficiency properties. We conclude the paper with a discussion of the error bounds for nonsmooth variational inequalities in the setting of Hadamard manifolds.