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Recent observation shows that general relativity (GR) is not valid in the strong regime. f(R) gravity, where R is the Ricci scalar, is regarded to be a good candidate able to cure the anomalies that appear in conventional general relativity. In this realm, we apply the equations of motion of f(R) gravity to a spherically symmetric spacetime with two unknown functions and derive original black hole (BH) solutions without any constraints on the Ricci scalar as well as on the form of f(R) gravity. Those solutions depend on a convolution function and are deviating from the Schwarzschild solution of the Einstein GR. These solutions are characterized by the gravitational mass of the system and the convolution function that in the asymptotic form gives extra terms that are responsible to make such BHs different from GR. Also, we show that these extra terms make the singularities of the invariants much weaker than those of the GR BH. We analyze such BHs using the trend of thermodynamics and show their consistency with well-known quantities in thermodynamics like Hawking radiation, entropy, and quasilocal energy. We also show that our BH solutions satisfy the first law of thermodynamics. Moreover, we study the stability analysis using the odd-type mode and show that all the derived BHs are stable and have radial speed equal to one. Finally, using geodesic deviations, we derive the stability conditions of these BHs. [ABSTRACT FROM AUTHOR]