Abstract
In this article, we develop and study a new complex function space formed by varying the weights and exponents under a definite function. We investigate the geometric and topological characteristics of mapping ideals created using s -numbers and this complex function space. Also, the action of shift mappings on this complex function space has been discussed. Finally, we introduced an extension of Caristi’s fixed point theorem on it.
Highlights
Numerous researchers are attempting to extend the Banach fixed point theorem [1] in a realistic manner
Lebesgue spaces with variable exponents, L(r), include Nakano sequence spaces
Across the second half of the twentieth century, it was thought that these variable exponent spaces offered an adequate framework for the mathematical components of a variety of problems for which the traditional Lebesgue spaces were inadequate
Summary
Numerous researchers are attempting to extend the Banach fixed point theorem [1] in a realistic manner. Ey explored the conditions under which it generates pre-quasi Banach and closed space when endowed with a particular pre-quasi norm as well as the Fatou property of various pre-quasi norms on it They showed the existence of a fixed point for Kannan pre-quasi norm contraction mappings on it as well as on the pre-quasi Banach operator ideal formed from this sequence space’s s-numbers. Upper bounds for s-numbers of infinite series of the weighted v-th power forward shift operator on (Hw((rv)))ψ were introduced for some entire functions They evaluated Caristi’s fixed point theorem in (Hw((rv)))ψ.
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