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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Fixed Point Results for Integral Type Contractions in R-Metric Space
Author(s):
Samriddhi Ghosh, Ramakant Bhardwaj, Ritu Shrivastava, Vandana Rathore, Satyendra Narayan
Department of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: ritha98@gmail.com
Department of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: drrkbhardwaj100@gmail.com
Department of Mathematics,
Bahrain Polytechnic, Isa Town,
Kingdom of Bahrain
E-mail: ritu.shrivastava@polytechnic.bh
Faculty of Science and Technology,
Jagran Lakecity University, Bhopal, Madhya Pradesh,
India.
E-mail: drvandana@jlu.edu.in
School of Computer Science and
Technology,
Algoma University, Brampton, Ontario,
Canada.
E-mail: narayan.satyendra@gmail.com
Abstract:
The main aim of the research is to establish some invariant point (fixed point) results under the purview of R-Metric Spaces, for integral type R-contractive mappings. To serve this purpose, concepts of R-continuity, R-convergence and R-preservation has been used. Finally, the obtained results has been used to deduce some invariant point results for Banach, Kannan and Chatterjea type mappings in R-Metric Space. Also some examples and applications have been illustrated to support the findings discussed.
Paper's Title:
Results Concerning Fixed Point for Soft Weakly Contraction In Soft Metric Spaces
Author(s):
Abid Khan, Santosh Kumar Sharma, Anurag Choubey, Girraj Kumar Verma, Umashankar Sharma, Ramakant Bhardwaj
Department of Mathematics,
AUMP, Gwalior,
India.
abid69304@gmail.com
Department of Mathematics,
AUMP, Gwalior,
India.
sksharma1@gwa.amity.edu
Department of Computer Science,
Technocrats Institute of Technology,
Bhopal, MP,
India.
directoracademicstit@gmail.com
Department of Mathematics,
AUMP, Gwalior,
India.
gkverma@gwa.amity.edu
Department of Physics,
RJIT BSF Tekanpur, MP,
India.
ussharma001@gmail.com
School of Applied Science
AUK, WB,
India.
rkbhardwaj100@gmail.com
Abstract:
The basic objective of the proposed research work is to make people acquainted with the concept of soft metric space by generalizing the notions of soft (ψ,φ)-weakly contractive mappings in soft metric space, as well as to look at specific fundamental and topological parts of the underlying spaces. A compatible example is given to explain the idea of said space structure. The theory is very useful in decision making problems and secure transmission as fixed point provides exact output. The fixed-point theorems on subsets of Rm that are useful in game theoretic settings.
Paper's Title:
Random Fixed Point Result in Banach Space
Author(s):
1Anwesha Ghorai, 2Samriddhi Ghosh, 3Sneha Khandait, 4Aditya Ghosh, 5Ramakant Bhardwaj, 6Satyendra Narayan
1
Department of Mathematics,3Engineering
Science and Humanities department,
Thakur College of Engineering and Technology, Mumbai, Maharashtra,
India.
E-mail: sneha.khandait@tcetmumbai.in
4Department
of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: ghosh.aditya.iitg08@gmail.com
5Department
of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: drrkbhardwaj@gmail.com
6School
of Computer Science and Technology,
Algoma University, Brampton, Ontario,
Canada.
E-mail: narayan.satyendra@gmail.com
Abstract:
The present paper deals with an extension of classical fixed point theory using random variable for advancement because it has far-reaching applications in calculus, optimization, and stochastic processes. However, many nonlinear operators arise in applied mathematics which do not fulfill the strict contraction conditions of the classical Banach principle. This limitation has inspired the development of generalized non-contractive mappings. New generalized contractive-type conditions for random operators in a complete probability measure space as well as Banach space are established. The proposed conditions incorporate nonlinear, fractional, and minimum-type terms. Random fixed point theorem are proved for rational inequalities. These results not only generalize existing theorems, but also contribute to further development of functional analysis and its applications in mathematical modeling.
Paper's Title:
Optimal Conditions using Multi-valued G-Presic type Mapping
Author(s):
Deb Sarkar, Ramakant Bhardwaj, Vandana Rathore, and Pulak Konar
Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: debsarkar1996@gmail.com
Department of Mathematics, Amity
University, Kadampukur, 24PGS(N), Kolkata, West Bengal, 700135,
India.
E-mail: drrkbhardwaj100@gmail.com
School of Engineering and Technology,
Jagran Lakecity University, Bhopal, MP-462044,
India.
E-mail: drvandana@jlu.edu.in
Department of Mathematics,
VIT University, Chennai, Tamil Nadu-600127,
India.
E-mail: pulakkonar@gmail.com
Abstract:
In the present paper, some best proximity results have been presented using the concept of G-Presic type multi-valued mapping. These results are the extensions of Presic's theorem in the non-self mapping. A suitable example has also been given. Here, some applications are presented in θ-chainable space and ordered metric space.
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