In this paper, we extend relation-theoretic contraction principle due to Alam and Imdad to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely T-transitive binary relation, which improves the corresponding fixed point theorems especially due to:
The purpose of this study was to explore the relationship between body fat percentage with speed, agility and reaction-time of Bangladesh Krira Shikkha Protisthan (BKSP) male football players. To work on the purpose 16 football players who were in their age of 15 to 16 years and having training in BKSP, were recruited as the subjects. The data on the variables such as percentage of body-fat (BF), speed, agility and reaction-time (RT) were collected by using standard tools and techniques. BF were obtained by using skinfold caliper, 50 meters dash was used to test the speed of the subjects, agility was obtained by using 6×10 meters shutter run, a software (Topend sports) was used to record reaction-time of the participants. After collecting data, it was analyzed by using SPSS-23 (IBM, United States). The results of the study documented that there is no significant relationship exists between percentage of bodyfat with speed, agility and reaction-time of BKSP male football players.
In this article, we carry out some observations on existing metrical coincidence theorems of Karapinar et al. (Fixed Point Theory Appl. 2014:92, 2014) and Erhan et al. (J. Inequal. Appl. 2015:52, 2015) proved for Lakshmikantham-Ćirić-type nonlinear contractions involving (f , g)-closed transitive sets after proving some coincidence theorems satisfying Boyd-Wong-type nonlinear contractivity conditions employing the idea of (f , g)-closed locally f-transitive binary relation.
We observe that all the results involving a-type F-contractions are not correct in their present forms. In this article, we prove some fixed point results for extended Fweak contraction mappings in metric and ordered-metric spaces. Our observations and the usability of our results are substantiated by using suitable examples. As an application, we prove an existence and uniqueness result for the solution of a first-order ordinary differential equation satisfying periodic boundary conditions in the presence of either its lower or upper solution.
In this paper, we introduce the notion of generalized L-contractions which enlarge the class of ℒ-contractions initiated by Cho in 2018. Thereafter, we also, define the notion of L∗-contractions. Utilizing our newly introduced notions, we establish some new fixed-point theorems in the setting of complete Branciari’s metric spaces, without using the Hausdorff assumption. Moreover, some examples and applications to boundary value problems of the fourth-order differential equations are given to exhibit the utility of the obtained results.
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