A Generalization of Caristi's Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space. (7th June 2021)

• Record Type: Journal Article
• Authors: Bakery, Awad A.; El Dewaik, M. H.
• Other Names: Isik Huseyin Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-06-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/9919420
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Suppose p n be sequence of positive reals. By H w p n, we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞, for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi's fixed point theorem in H w p n .