The purpose of the current study is to find exact travelling wave solutions of the Rosenau equation. By the use of the extended auxiliary equation method, various exact solutions are obtained in terms of Jacobi elliptic functions and exponential functions. Moreover, several solitary and periodic wave solutions are given as special cases. When the parameters take some values, some graphical illustrations are shown in order to understand the behaviour of these new solutions. Furthermore, we compare our solutions with some familiar solutions, which can be considered as special cases.
The current manuscript investigates the exact solutions of the modified Benjamin-Bona-Mahony (BBM) equation. Due to its efficiency and simplicity, the modified auxiliary equation method is adopted to solve the problem under consideration. As a result, a variety of the exact wave solutions of the modified BBM equation are obtained. Furthermore, the findings of the current study remain strong since Jacobi function solutions generate hyperbolic function solutions and trigonometric function solutions, as liming cases of interest. Some of the obtained solutions are illustrated graphically using appropriate values for the parameters.
<abstract><p>This paper presents a novel concept of $ G $-Hardy-Rogers functional operators on metric spaces endowed with a graph. It investigates sufficient circumstances under which such a mapping becomes a Picard operator. As applications of the principal idea discussed herein, a few important corresponding fixed point results in ordered metric spaces and cyclic operators are pointed out and analyzed. For upcoming research papers in this field, comparative graphical illustrations are created to highlight the pre-eminence of proposed notions with respect to the existing ones.</p></abstract>
We prove the existence of positive radial solutions to the problemwhere ∆pu = div(|∇u| p−2 ∇u), N > p > 1, Ω = {x ∈ R N : |x| > r 0 > 0}, f : (0, ∞) → R is p-superlinear at ∞ with possible singularity at 0, and λ is a small positive parameter. A nonexistence result is also established when f has semipositone structure at 0.
<abstract><p>In this note, by using basic properties of the recently introduced concepts of generalized metric spaces, new conditions for the existence of a fixed point for weakly type contractive operator which sends a closed subset into the ambient space under consideration are examined. Our obtained result extends and unifies its corresponding ideas in metric and modular spaces. A comparative non-trivial example is provided to show the novelty and preeminence of our proposed notion.</p></abstract>
In this paper, we introduce the relation between statistical geometric mean and statistical summability (C, 1) by using Caushy inequality. Then, we investigate a Korovkin type approximation by using G-statistical convergence for a sequence of positive linear operators.
The applications of non-zero self distance function have recently been discovered in both symmetric and asymmetric spaces. With respect to invariant point results, the available literature reveals that the idea has only been examined for crisp mappings in either symmetric or asymmetric spaces. Hence, the aim of this paper is to introduce the notion of invariant points for non-crisp set-valued mappings in metric-like spaces. To this effect, the technique of κ-contraction and Feng-Liu’s approach are combined to establish new versions of intuitionistic fuzzy functional equations. One of the distinguishing ideas of this article is the study of fixed point theorems of intuitionistic fuzzy set-valued mappings without using the conventional Pompeiu–Hausdorff metric. Some of our obtained results are applied to examine their analogues in ordered metric-like spaces endowed with an order and binary relation as well as invariant point results of crisp set-valued mappings. By using a comparative example, it is observed that a few important corresponding notions in the existing literature are complemented, unified and generalized.
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