In this paper, we prove the existence of solutions for a variational-like inequality and a generalized variational-like inequality in the relaxed η-α pseudomonotone and strictly η-quasimonotone cases in Banach spaces by using the KKM technique. The results presented in this paper improve and extend some corresponding results of several authors. [ABSTRACT FROM AUTHOR]
RANDOM fields, MATHEMATICAL inequalities, BANACH spaces, LAW of large numbers, DIFFERENCE sets, MARCINKIEWICZ-Orlicz spaces, MATHEMATICAL models, NUMERICAL analysis
Abstract
We obtain inequalities for sums of adapted random fields in p-uniformly smooth Banach spaces, and we extend Kolmogorov and Marcinkiewicz-Zygmund strong laws for blockwise α-martingale difference fields. [ABSTRACT FROM AUTHOR]
In this work, we introduce the class of α-ψ-Geraghty contraction as well as generalized α-ψ-Geraghty contraction mappings in the context of generalized metric spaces where ψ is an auxiliary function which does not require the subadditive property and set up some fixed point results for both classes individually. Our results will extend, improve and generalize several existing results in the literature. [ABSTRACT FROM AUTHOR]