en عمومى General پژوهشي Research paper <div style="text-align: justify;">In this paper we introduce rough ϕ-convergence of real numbers as a generalization of rough convergence as well as ϕ-convergence. We study some of its basic properties and relations of the above convergence concept with already known different types of convergence.<br> In 2001, H.X.Phu proved that &ldquo;The diameter of a r-limit set is not greater than 2r&rdquo;. We investigate the above result for rough ϕ-convergence by introducing r - ϕ limit set and surprisingly the result comes out to be not true. So our main aim is to find out the different behaviour of the new convergence concept based on r - ϕ limit set.</div> Rough convergence, ϕ−Convergence, r − ϕ-Convergence, r − ϕ Limit set. 145 153 http://ijmsi.ir/browse.php?a_code=A-10-203-2&slc_lang=en&sid=1 Chiranjib Choudhury chiranjib.mathematics@tripurauniv.in; chiranjibchoudhury@gmail.com 100319475328460012358 100319475328460012358 No Department of Mathematics, Tripura University (A Central University), Suryamaninagar-799022, Agartala, India Shymayal Debnath shyamalnitamath@gmail.com; debnathshyamal@tripurauniv.ac.in 100319475328460012359 100319475328460012359 No Department of Mathematics, Tripura University (A Central University), Suryamaninagar-799022, Agartala, India Ayhan Esi ayhan.esi@ozal.edu.tr; aesi23@hotmail.com 100319475328460012360 100319475328460012360 Yes Department of Basic Eng. Sci. (Math. Sect), Malatya Turgut Ozal University, 44100, Malatya, Turkey