Applications of Composite Convolution Operators

The Composite Convolution Operator is an operator which is obtained by composing Convolution operator with Composition operator. Volterra composite convolution operator is a composition of Volterra convolution operator and Composition operator. The Composite Convolution Operators and Composite Convolution Volterra operators have been defined by using the Expectation operator and Radon-Nikodym derivative. In this paper an attempt has been made to investigate applications of Composite Convolution Operators (CCO) in Integral Convolution Type Equations (ICTE). The study may explore a new technique to solve Fredholm Convolution type integral equations and Volterra Convolution type integral equations. Some methods for solving integral convolution type equations by using Composite Convolution Operators have also been studied. For integral convolution type equations, theorems on existence, uniqueness and estimates for solution have also been proved without any restriction for the parameter. In order to determine the solution by the method of successive approximations in this paper, I have made use of the concept of the Resolvent Kernel to obtain Neumann Series. The Banach Contraction Principle has also been used to obtain some results. The method of Variational Iteration has been applied to find out the approximate solution of integral equations by using Composite Convolution Operators. In this paper Numerical Methods have also been adopted for solution of these integral equations. Fourier transform has been used to solve Integral convolution type equations and Laplace transform has been applied to solve Volterra convolution type equations

A Common Unique Random Fixed Point Theorems in S – Metric Spaces

In this paper, we present some new definitions of S – metric spaces and prove some random fixed point theorem for two random functions in complete    S – metric spaces. We get some improved versions of several fixed point theorems in S – metric spaces. Key words: - metric space, S – metric space, common fixed point theorem

Professional Development of Teachers in Higher Education

In today’s high tech world the spine of a developed society is its education system. The efficacy and strength of an educational system in turn lies upon its teachers. Effective teaching comprises of inculcating problem solving strategies, moral values and ability to make social adjustments in the tender minds of young generation. Thus teaching becomes a fulfilling journey that gives an amazing chance to shape the future of a society. It becomes quite necessary for a teacher to cultivate the habit of self-assessment, improve interactions; develop reflective strategies etc. to steer students towards healthy reflexive skills. The paper explores the various objectives, policies and implementation of policies made for the professional development of teachers in higher education departments. Since teacher education and professional development are the synonyms of each other it is better to pay attention to this field if we really want to make our education system efficient. This paper throws light on the efforts government has made by drafting policies for teacher education in India and what loopholes have been left in their implementation. There are also some suggestions to cover the loopholes left in the implementation of existing policies for professional development of teachers in India. Keywords:  DIET (District Institute of Education and Training), IASE (Institute of Advanced Studies in Education), CTE (College of Teacher Education

Some Fixed Point and Common Fixed Point Results in L – Space

There are several theorems are prove in L – space, using various type of mappings. In this paper, we prove some fixed point theorem and common fixed point theorem in L- space using different, symmetric rational mappings. Keywords: Fixed point, Common Fixed point, L – space, Continuous mapping, Self Mapping, Weakly Compatible Mappings

Fixed Point Theorem in Intuitionistic Fuzzy Metric Space by Using Occasionally Weakly Compatible Maps in Rational Form

In this paper we have generalized the result of Kamal Wadhwa and Hariom Dubey by using occasionally weakly compatible maps using intuitionistic fuzzy metric space. The concept of compatible maps introduced by Kramosil and Michalek and weakly compatible maps in fuzzy metric space is generalized by A. Al. Thagafi and Nasser Shahzad by introducing the concept of occasionally weakly compatible mappings. Keywords: Fixed point, intuitionistic fuzzy metric space, compatible mappings

COMMON FIXED- POINT THEOREM IN NON-ARCHIMEDEAN INTUITIONISTIC FUZZY METRIC SPACE BY USING SUBCOMPATIBLE MAPS OF TYPE (α) WITH SIX MAPS

In this paper, we have generalized the result of Ferhan Sola Erduran [15] and Anupama Gupta [3] using sub compatible map of type (α) and subsequent continuity. We established a common fixed-point theorem for six maps

Common Unique Fixed Point Theorem for Random Operators in Hilbert Space

The object of this paper is to obtain a common fixed point theorem for four continuous random operators by considering a sequence of measurable functions satisfying certain contractive condition in separable Hilbert space. Keywords: Separable Hilbert space, random operators, common random fixed point, rational inequality.

Assessment of patient satisfaction after levonorgestral containing intrauterine system insertion in women with abnormal uterine bleeding

Background: Abnormal uterine bleeding is a common gynecological complaint affecting 10-30% of reproductive-aged women and it can result from different causes which adversely affects the woman’s quality of life, necessitating its appropriate and adequate management. Among all the pharmacological and surgical management options of AUB. LNG-IUS is emerging as a safer and effective treatment option of AUB. However apprehension about discomfort associated with the use of intrauterine device leads to its untimely removal. Aim of current study was to conduct a prospective qualitative study to observe the level of patient satisfaction with the use of LNG-IUS in patients with abnormal uterine bleeding.Methods: This study was conducted in the department of obstetrics and gynecology, MGM medical college and M.Y. Group of Hospitals, Indore from March 2017- March 2018. Follow up was done at 1, 3, 6 months.Results: In our study, majority of the women (90%) had improvement in their abnormal uterine bleeding along with significant increase in mean hemoglobin level from7.30+1.29 gm%  to 8.71+1.27 gm% at the end of six months. 86.66% of these patients were very satisfied with the use of LNG IUS,Conclusions: LNG-IUS is an effective device for medical management of AUB and it should be used as the first line therapy for the same. It should always be considered before surgical interventions. It yields promising result in terms of patient satisfaction.