New Class of Generalized Hermite-Hadamard Type Inequalities

Forschungsarbeit aus dem Jahr 2024 im Fachbereich Mathematik - Analysis, , Sprache: Deutsch, Abstract: The graphical elegance of fractal theory takes into account the development's achievability and exceptionalism. Due to its fascinating existence in the mathematical fields of sciences, there is a clear association between fractal sets and convexity. In this proposal, we will present generalized convexity and related integral inequalities on a fractal set R? ( 0 < ? ? 1). In the context of the Beta function, this research presents a new class of generalized Hermite-Hadamard type inequalities. This research contributes significant results of novel versions of fractal Hölder's and Young's inequalities. We derive some general conclusions that capture novel results under investigation. One more remarkable contribution of the study is that two novel auxiliary results along with Trapezoidal and Midpoint type inequalities are provided. Hence, these new results will lead us to generalization of prior results.

Iram Javed, born on June 9, 1998, embarked on a remarkable academic journey that has taken her from the classrooms of Pakistan to the prestigious halls of Beihang University in China. Her dedication to education, outstanding achievements, and scholarly contributions have marked her as a rising star in the academic world. Her educational foundation was laid in Pakistan, where she displayed an early passion for learning. Growing up, she exhibited a keen interest in academics, paving the way for a promising future. Her early education in Pakistan not only nurtured her intellectual curiosity but also instilled in her a strong work ethic. Iram's pursuit of knowledge continued through her undergraduate years, culminating in a noteworthy achievement. She earned a bronze medal for her outstanding academic performance and an impressive Cumulative Grade Point Average (CGPA). Her commitment to excellence set the stage for further accomplishments in her academic journey. Building on her success in her bachelor's degree, Iram pursued a master's degree, where her academic prowess continued to shine. During this phase, she delved into research and made substantial contributions to her field. She published three articles, showcasing not only her commitment to academia but also her ability to contribute valuable insights to the scholarly community. The culmination of Iram Javed's academic journey led her to secure a coveted position in a Ph.D. program at Beihang University, one of China's premier institutions. What makes her journey even more extraordinary is the fact that she secured a Ph.D. position with a full Chinese Government Scholarship, a testament to her academic excellence and potential. Iram is currently immersed in her Ph.D. studies at Beihang University, where she continues to demonstrate her dedication to advancing knowledge in her chosen field. Her research pursuits are not only contributing to her personal growth but also adding to the body of academic knowledge on an international scale. As Iram continues her academic pursuits, her story serves as an inspiration to aspiring researchers and underscores the limitless possibilities that dedication to learning can unlock.