The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

This study involved the treatment of textile wastewater contaminated with direct blue 15 dye (DB15) using a heterogeneous photo-Fenton-like process. Bimetallic iron/copper nanoparticles loaded on bentonite clay were used as heterogeneous catalysts and prepared via liquid-phase reduction method using eucalyptus leaves extract (E-Fe/Cu@BNPs). Characterization methods were applied to resultant particles (NPs), including SEM, BET, and FTIR techniques. The prepared NPs were found with porous and spherical shapes with a specific surface area of particles was 28.589 m2/g. The effect of main parameters on the photo-Fenton-like degradation of DB15 was investigated through batch and continuous fixed-bed systems. In batch mode, pH, H2O2 dosage, DB15 c

Abstract. Nano-continuous mappings have a wide range of applications in pure and applied sciences. This paper aims to study and investigate new types of mappings, namely nano-para-compact, completely nano-regular, nano-para-perfect, and countably nano-para-perfect mappings in nano-topological spaces using nano-open sets. We introduce several properties and basic characterizations related to these mappings, which are essential for proving our main results. Additionally, we discuss the relationships among these types of mappings in nano-topological spaces. We also introduce the concept of nano-Ti-mapping, where i = 0, 1, 2, nano-neighborhood separated, and nano-functionally separated, along with various other definitions. We explore the relat

Abstract. The purpose of this work is to introduce and investigate new concepts of mappings namely nano paracompactmappings, nano locally limited, nano h-locally limited and finally nano-perfect in nano topology by using nano-closed sets. As well as, the relation between these concepts of mappings have been study in nano topology. Additionally, the nano topology groups of the types and advances results which are introduces in this work are very vital. We also presented the type of nano Lindeloff mappings, and the relations of them was introduce and discussed with several characteristics related it. Nano morphism also introduce.

In this paper, we shall introduce a new kind of Perfect (or proper) Mappings, namely ω-Perfect Mappings, which are strictly weaker than perfect mappings. And the following are the main results: (a) Let f : X→Y be ω-perfect mapping of a space X onto a space Y, then X is compact (Lindeloff), if Y is so. (b) Let f : X→Y be ω-perfect mapping of a regular space X onto a space Y. then X is paracompact (strongly paracompact), if Y is so paracompact (strongly paracompact). (c) Let X be a compact space and Y be a p*-space then the projection p : X×Y→Y is a ω-perfect mapping. Hence, X×Y is compact (paracompact, strongly paracompact) if and only if Y is so.

In this paper, we will introduce and study the concept of nano perfect mappings by using the definition of nano continuous mapping and nano closed mapping, study the relationship between them, and discuss them with many related theories and results. The k-space and its relationship with nano-perfect mapping are also defined.

The aims of this thesis are to study the topological space; we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore, we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied. On the other hand, we studied weakly/ strongly forms of ω-perfect mappings, namely -ω-perfect mappings, weakly -ω-perfect mappings and strongly-ω-perfect mappings; also, we investigate their fundamental properties. We devoted to study the relationship between weakly -ω-perfect mappings and strongly -ω-perfect mappings. As well as, some new generalizations of some definitions wh

Fuzzy orbit topological space is a new structure very recently given by [1]. This new space is based on the notion of open fuzzy orbit sets. The aim of this paper is to provide applications of open fuzzy orbit sets. We introduce the notions of fuzzy orbit irresolute mappings and fuzzy orbit open (resp. irresolute open) mappings and studied some of their properties. .