On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field

Abstract

The studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction. Sometimes the associated multiplier sequence delays the rate of convergence of a sequence. In the present paper, the classical paranormed sequence spaces have been introduced and proved that the spaces are⋆-complete. By using the notion of multiplier sequence, theα-,β-, andγ-duals of certain paranormed spaces have been computed and their basis has been constructed.

A Generalization of Hermite–Hadamard–Fejer Type Inequalities for the p -Convex Function via α -Generator

“…Te non-Newtonian calculi are useful mathematical tools in science, engineering, and mathematics and provide a wide variety of possibilities, as a diferent perspective. Specifc felds of application include fractal theory, image analysis (e.g., in biomedicine), growth/decay processes (e.g., in economic growth, bacterial growth, and radioactive decay), fnance (e.g., rates of return), the theory of elasticity in economics, marketing, the economics of climate change, atmospheric temperature, wave theory in physics, quantum physics and the Gauge theory, signal processing, information technology, pathogen counts in treated water, actuarial science, tumor therapy in medicine, materials science/engineering, demographics, and diferential equations [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Some basic properties of bigeometric calculus and its applications in numerical analysis

“…We refer to Grossman and Katz [15], Stanley [19], Bashirov et al [3,4], Grossman [14] for elements of multiplicative calculus and its applications. An extension of multiplicative calculus to functions of complex variables is handled in Bashirov and Rıza [2], Uzer [23], Çakmak and Başar [10], Çakir [6], Kadak et al [17,18], Tekin and Başar [20], Türkmen and Başar [21,22]. Kadak and Özlük [16] studied the generalized Runge-Kutta method with respect to non-Newtonian calculus.…”

Application of geometric calculus in numerical analysis and difference sequence spaces

“…In [10], Kadak and Özlük studied the generalized Runge-Kutta method with respect to non-Newtonian calculus. Kadak et al [8,9] studied certain new types of sequence spaces over the Non-Newtonian Complex Field.…”